Aircraft propulsion system with turbine engine coupled to an electric generator the power of which is limited as a function of engine speed

An aircraft propulsion system comprising:

• a gas turbine engine with a combustion chamber and an engine spool, the engine spool including a turbine downstream of the combustion chamber, a compressor upstream of the combustion chamber and a transmission shaft for driving the compressor via the turbine;
• a control system;
• a member for determining a current engine speed of the engine spool;
• and
• a rotary machine coupled to the transmission shaft for generating electrical power by taking off mechanical power from the transmission shaft,
• wherein the control system is configured to limit a current electrical power generated by the rotary machine at least when the engine spool is in the acceleration phase, to a maximum authorized power, the maximum authorized power being function of the current engine speed before acceleration, and
• wherein the propulsion system comprises a device for determining the current electrical power generated by the rotary machine, the control system being configured to establish the engine speed above an idle speed which is a function of the current electrical power.